Exact Moderate and Large Deviations for Linear Random Fields

TL;DR

This paper derives precise asymptotic formulas for moderate and large deviations in linear random fields with independent innovations, aiding in the analysis of nonparametric regression and limit theorems.

Contribution

It extends existing methods to establish exact deviation asymptotics for linear random fields, enhancing theoretical understanding and applications.

Findings

Derived exact asymptotics for deviations in linear random fields.

Applicable to nonparametric regression with random field errors.

Provides tools for strong limit theorems in spatial statistics.

Abstract

By extending the methods in Peligrad et al. (2014a, b), we establish exact moderate and large deviation asymptotics for linear random fields with independent innovations. These results are useful for studying nonparametric regression with random field errors and strong limit theorems.